I went home and ran a program under no load, and the issue was still present. I even ran the code in Mach3 with the machine off and ob :)served the shift in the DROs.
I then started studying the gcode. I discovered that these offsets were in the gcode, and each corner approach involves over 30 lines of code. So, it appears the machine is just doing what the code is telling it to do, but why is the gcode doing this?